The invention relates to etched foil heaters, and particularly relates to etched foil heaters of the low voltage type. In its most immediate sense, the invention relates to high output, low voltage etched foil heaters for applications in which a comparatively large area must be heated.
Etched foil heaters use conductive foil that is etched to form a serpentine pattern. During manufacturing, the foil is mounted to a backing and then etched into the desired pattern. The etched foil is then laid up in a dielectric matrix (e.g. silicone), connections (e.g. conductive foil tabs or wires) are led out of the matrix, and the matrix is then cured (removing the backing if necessary).
In an etched foil heater element, the conductive path is quite wide as compared to its thickness. Such a heater develops "hot spots" and "cold spots" at locations where the path changes direction. This is particularly evident at locations where the path makes a 180.degree. turn around a small radius.
Such hot spots and cold spots are caused by a phenomenon known as "current crowding". When electric current flows in a straight line through a wide foil conductor, the current density is fairly constant across the width of the conductor. However, when such a wide foil conductor changes direction, and particularly when it makes a 180.degree. turn, the current density is much higher at the inside of the turn. In general, this is because the conductive path has a minimum length--and therefore a minimum resistance--at the inside of the turn, and the electric current tends to flow along the path of least resistance. This increased current density produces a hot spot at the inside of the turn, and it can be shown that the heat flux (in watts/cm.sup.2) at a particular turn radius is approximately proportional to the inverse square of the turn radius. Put another way, the inside of each turn will have an excessive current density (high heat flux) and the outside of each turn will have a low current density (low heat flux). Therefore, at each 180.degree. turn, an etched foil heater will have a temperature gradient across the turn; the inside radius of the turn will be hotter than the outside radius.
In typical etched foil heater patterns, the magnitude of this temperature gradient is significant. As a result, the phenomenon of current crowding limits the maximum width of the foil conductor. This limitation, in turn, has undesirable consequences, especially when the heater is of the low voltage, high output type and is used for a low temperature application.
These consequences flow from two characteristics of a heater used for high output, low voltage applications: 1) the resistance of the heater element must be low to produce a high output; and 2) the resistance of a conductor is inversely proportional to the conductor's cross-sectional area. Because of these two characteristics, limiting the width of the foil (to in turn limit the temperature gradient across the turns of the heater element) means the foil must be thicker to keep the overall heater element resistance sufficiently low. This reduces the foil's base area or "footprint", which is critical to good heat transfer into the matrix. This also makes the foil stiffer and less tolerant of thermal expansion effects (which tend to delaminate the heater element from the matrix in which it is enclosed).
One approach to minimizing current crowding is to break the wide foil path into many parallel paths. However, when the current path is broken up into many relatively narrow parallel paths the heater element becomes more difficult to handle during the manufacturing process. This is because the many narrow foil strips can easily become twisted, tangled and damaged as they catch on each other. Furthermore, as the foil strips become thicker and narrower, they increasingly take on the characteristics of wire conductors, which would have a relatively high local heat flux out of the heater element and into the surrounding matrix. This is because the foil has a relatively small footprint, so that the heat produced by the heater element is distributed over a comparatively small surface area. Such a relatively high local heat flux can produce relatively high temperatures, which reduce life and reliability.
It would be advantageous to provide a low voltage, high output (low resistance), etched foil heater for applications requiring a uniform heat flux at a low temperature, in which the heater element would be easy to handle.
The invention proceeds from the realization that the wide serpentine conductor of an etched foil heater can be divided up into a plurality of parallel strips having the equivalent overall resistance. Therefore, in a serpentine etched foil heater in accordance with the invention, the heater comprises a segmented serpentine conductor group made up of a plurality of spaced-apart elongated serpentine conductive strips that are connected in parallel and are everywhere aligned with each other. Because the single wide conductor has been replaced by a plurality of comparatively narrow ones, the current crowding effect is reduced within each individual path.
In the preferred embodiment, the widths of the conductive strips are selected to correspond to the radii of curvature that the conductive strips are required to assume. Therefore, a conductive strip that will lie at the most inside position of a 180.degree. turn is made narrowest, and a conductive strip that will lie along a larger radius of a 180.degree. turn is made wider. In practice, this means that the conductive strips are widest at the center of the conductor group and narrowest at the radially outermost edges of the conductor group. This is because the serpentine nature of the heater causes radially inwardly conductive strips to be located at radially outward positions at adjacent turn locations along the conductive path. The exact pattern of foil widths, from narrowest at the edges to widest in the center, is determined by an analysis that takes into account the current crowding heat flux (which follows the inverse square of the radius) and the thermal conductance of the foil (which tends to spread the heat within the wire). Advantageously although not necessarily, each conductive strip has a constant width, and all the conductive strips are kept equally long. This is conveniently accomplished by using an odd number of 180.degree. turns.
In the preferred embodiment, the heater is made easier to handle by physically interconnecting the parallel conductive strips. This is accomplished by bridging across adjacent strips using conductive regions that extend along lines of constant voltage. Because such regions have equal voltages at their endpoints, no current flows through them and they have no effect on the heat flux produced by the heater. This overcomes the handling difficulties that would ordinarily be associated with an etched foil heater element having many turns and many parallel conductive paths, and eliminates the need for a carrier such as KAPTON.RTM..